The collection of information relating to downhole conditions, commonly referred to as “logging,” can be performed by several methods including “logging while drilling” (“LWD”) and wireline logging. Downhole acoustic logging tools are often utilized to acquire various characteristics of earth formations traversed by the borehole. In such systems, acoustic waveforms are generated using a transmitter, and the acoustic responses are received using one or more receiver arrays. The acquired data is then utilized to determine the slownesses (velocities) of the formation to obtain a maximum slowness and a minimum slowness; and processing the maximum slowness and the minimum slowness obtained to determine the horizontal transverse acoustic anisotropy and the angular direction of the formation's maximum and minimum slownesses. The amount of anisotropy and the direction may be of use in well planning and formation evaluation; for example, to direct perforation guns or assess wellbore stability.
In order to determine the acoustic anisotropy slowness values, conventional techniques apply model fitting. In LWD configurations that collect many slowness measurements (perhaps 8 or more) randomly in azimuth around the borehole, one technique fits a periodic model with a cycle period of 180 degrees to these measurements. The resulting model's fit phase and amplitude are used to measure the anisotropy. Also, wireline logging may use an Alford rotation model to measure anisotropy from only four azimuthal slowness measurements, commonly acquired in a “cross-dipole” configuration.
However, such fitting methods are disadvantageous because the local formation anisotropy mechanism may be complex and, thus, may deviate from these model assumptions (in particular that the measured slowness varies sinusoidally with azimuth). Also, a non-random collection of azimuth measurements may bias the model results, thereby resulting in inaccurate slowness determinations.